We have studied two regions of doubly closed shell nuclei over the nuclear chart: stable nuclei with N ~ Z around 40Ca and highly neutron-rich ones close to drip-line above the 132Sn shell closure. Both experimental and theoretical works have been performed for each of these mass regions. The experimental part includes three works: (i) high energy characterization of the Compton suppressed Clover detector, (ii) In-beam gamma-ray spectroscopic studies of high spin states of 35Cl in mass 40 region and (iii) X- and gamma- ray spectroscopic studies of fission fragments of 252Cf spontaneous...